Variable Gap Tapering for LCLS-II Undulators

Transcription

1 Variable Gap Tapering for LCLS-II Undulators Heinz-Dieter Nuhn April 12, 2018 Continuous Taper, Apr 12,

2 Schematic Layout of LCLS-II New So; X- ray FEL with adjustable- gap undulator line (SXR) New Hard X- ray FEL with adjustable- gap undulator line (HXR) ~4.0 GeV kev gun- 2 gun- 1 Und. Hall SXR Dump sectors 0-10 SCRF Linac ~4 GeV Up to 1 MHz sectors Cu Linac GeV 120 Hz HXR kev kev 1-25 kev Continuous Taper, Apr 12,

3 LCLS-II SXR and HXR Component Layouts Cell Length: ± m Space for 2-stage HXRSS Location for upgraded HXRSS Space for SXRSS Cell Length: ± m Space for 3 Polarization Control Undulators Continuous Taper, Apr 12,

4 Undulator System Layout SXR Undulator Line HXR Undulator Line Continuous Taper, Apr 12,

5 LCLS-II SXR Undulator (HPU) Continuous Taper, Apr 12,

6 LCLS-II HXR Undulator (VPU) Continuous Taper, Apr 12,

7 LCLS-II Undulator Dimensions and Ranges Parameter SXU / SCRF SXU / Cu HXU / SCRF HXU / Cu Unit Undulator period length mm Total segment length m Number of periods per strong back X-ray energy range, required* kev Undulator operational gap range mm Undulator parameter range, K Electron energy range, operational GeV Maximum gap taper µm *at 4.0 GeV, the lower limit is 0.25 and 1.5 kev, respectively Continuous Taper, Apr 12,

8 LCLS Step Taper Only Continuous Taper, Apr 12,

9 LCLS-II Gap Encoder Difference [um] (Downstream Upstream) Continuous Taper, Apr 12,

10 LCLS-II Undulator Segment 300 µm taper over 3.4-m segment length (~88 µrad) Undulator Segment Strongbacks Upstream gap encoder Downstream gap encoder K/K ( g/ λ u ) g/ λ u Continuous Taper, Apr 12,

11 Large Taper Ranges at LCLS-II Continuous Taper, Apr 12,

12 SXU-007 Field Measurements: (1) Untapered <K pole > = ± K eff = ± Single Pole Hall Probe Data z 0 up,pole z 0 dn,pole K pole ( z pole )= Δ z pole /2π e/ m e c Δ z pole = z 0 dn,pole z 0 u z pole 1/2 ( z 0 dn,pole + z 0 Continuous Taper, Apr 12,

13 SXU-007 Field Measurements: (2) Tapered Measured K pole values for SXU tapers of +100 µm and +300 µm and reversed taper of -100 µm at 8 mm and 20 mm gap. Difference between tapered and untapered K pole values is only according to gap change. (No distortion at large tapers observed) Continuous Taper, Apr 12,

14 Field Evaluations for Tapered Undulators Standard calculations of phase shake and total phase assume constant beam energy and can not be applied to tapered undulators. Instead assume that taper is necessary because of energy loss along undulator segment, i.e., A value for can be found that minimizes the change of phase advance per period. α γ γ=γ(z)= γ start (1 α γ(z)= γ start f tp (z) f tp (z)={ 1&for z< z α γ ( z Continuous Taper, Apr 12,

15 Phase Calculations The phase slippage for changing energy along undulator segment is φ taper (z)= 2π/ λ u (1+ 1/2 K( g start ) 2 ) 0 z 1/ f tp ( z ) 2 (1+ The field integrals are calculated as usual I1x(z)= 0 z B x ( z )d z I1y(z)= 0 z B y ( z )d z The slopes and trajectories are d/dz y(z)= 1/ (Bρ) start d/dz I1x( z x(z)= 1/ (Bρ) start )/ f tp ( z ) I (Bρ) start = γ start m c/e y(z)= 1/ (Bρ) start 0 z I1x( z x(z)= 1/ (Bρ) start )/ f tp ( z ) 0 z d z Continuous Taper, Apr 12,

16 Phase Measurements φ taper (z)= 2π/ λ u (1+ 1/2 K( g start ) 2 ) 0 z 1/ f tp ( z ) 2 (1+ ( e/m c ) 2 ( I1x( z ) blue: untapered red: taper 300 µm, = α γ Difference During free space travel after undulator, phase advance per unit length is longer for larger regular tapers due to lower electron energies. ~360 degxray per period in both cases d/dz ( φ tapered φ untapered )= 360/ λ u (1+ 1/2 K( g start ) 2 ) ( 1/ For SXU-007, at 300 µm taper and 8 mm gap (1 α γ ) 2 1) d/dz ( φ tapered 38.6 degxray / m φ untapered )= Continuous Taper, Apr 12, 2018 This will be corrected with a phase shifter. 16

17 SXU-007 Trajectories BBA corrected horizontal and vertical trajectories for +300 µm SXU taper based on field measurements. Only insignificant deviation from untapered trajectories observed. Continuous Taper, Apr 12,

18 Summary The LCLS-II undulators allow continuous gap tapering Limits are ±300 µm over segment length (~±88 µrad) SXU taper measurements look promising: If adjusted to compensate for energy loss, tapering will mostly change the downstream phase advance will only slightly increase overall phase shake will not significantly steer the electron beam HXU (vertically polarizing undulator) taper measurements will follow soon Continuous Taper, Apr 12,

19 Thank you for your attention! Continuous Taper, Apr 12,